Introduction to the Mori Program

Introduction to the Mori ProgramThis book started as a collection of personal notes that I made to help me to un­ derstand what we call the Mori program, a program that emerged in the last two decades as an effective approach toward the biregular and/or birational classifica­ tion theory of higher-dimensional algebraic varieties. In some literatures the Mori program restrictively refers to an algorithm, called the minimal model program, to produce minimal models of higher-dimensional algebraic varieties. (Classically, the construction of minimal models was known only for algebraic varieties of di­ mension less than or equal to 2. ) Here in this book, however, we use the word in a broader sense to represent a unifying scheme that is a fusion of the minimal model program and the so-called Iitaka program. As such, I had no hesitation to, or rather even made elaborate efforts to, extract nice arguments from the existing literature whenever it seemed appropriate to fit them into a comprehensible development of the theory, even to the extent of copying them literally word by word. I am particularly aware of the original sources of the subject matters in the following list: Chapter 1. Barth-Peters-Van de Ven [I], Beauville [1], Clemens-Kollar-Mori [I], Griffiths-Harris [1], Hartshorne [3], litaka [5], Kawamata-Matsuda­ Matsuki [1], Kodaira [2][3][4][5], Kollar [5], Mori [2][3], Reid [9], Shafarevich [I], Wilson [I] Chapter 2. Iitaka [2] [3] [5], Kawamata [1][2], Vojta [1] VI Preface Chapter 3.

The first book in this extremely important and active area of research; likely to become a key resourceAuthor presents the theory in an easy and understandable way with lots of background motivationPrerequisites are kept to a minimum, enabling readers to quickly orient themselves with the theory